Do you mean in my "Do Call Options Have High Expected Returns?" piece or elsewhere?

I haven't seen such evidence anywhere.

Shouldn't all capital markets have about equal expected returns? Or do you mean that some markets have higher returns due to higher systemic risk?

On the efficient market story it doesn't matter for returns whether you invest in the US or abroad. But (1) the non-capital investments of philanthropists with your values are particularly tied up in the US, and so if it make no difference it seems bad to take on the extra correlation, (2) prices really do look high right now in the US, and there are plausible stories about how that could happen in the existing financial system, so even if you only assign those stories a modest probability, it seems worth moving in that direction.

prices really do look high right now in the US, and there are plausible stories about how that could happen in the existing financial system

Do you have a short summary? I could probably fill in the details from even a one line description. I know of several such stories but would be interested in hearing which you find plausible. Certainly there are also several popular but false ones (e.g. Schiller PE)

My main reason for pessimism is the comparison between US equities and international equities; I guess that forward P/E's are higher in the US than elsewhere. This is largely based on the high Schiller PE / current profit margins in the US though (along with comparable P/E and high P/B ratios), so it would be good to know if you think this is a bad basis for extrapolation.

The "plausible stories" I was referring to were about how mispricings could persist. My understanding is that many investors' allocations between US and international equities isn't very flexible. Such investors could make up a large enough majority and short-selling could be unattractive enough that a moderate mispricing could persist. There are also principal-agent problems related to benchmarking, and well-documented market optimism about continuing growth vs. regression to the mean, that seem to point in the same direction.

But I haven't thought about this angle very much either, so it would be good to know if you think these mispricings would get fixed.

The US market is slightly more expensive on a forward PE basis. However, Schiller PE is nonsense. For example, buybacks have become much more commonplace since the early 1980s, which increase the secular EPS growth rate (by reducing the dividend yield). The schiller PE does not adjust for this however; it assumes EPS will revert to their previous level, rather than profits reverting to their previous level. It also ignores the effects of dilution. Many companies issued a lot of equity during the crisis (especially banks). These companies now have much lower EPS as a result, even if profits returned, yet schiller PE implicitly assumes that their EPS will magically revert to their previous level. Hopefully this is clear; if not I can explain when we skype.

(There are several other problems with schiller PE).

Yes many investors can't re-allocate between markets but there are some whose entire job is this. I'm not sure about the end result of this.

4) These models are all correlated ~0.8 with 10yr returns, so you'd need to think something pretty substantial had changed for them to break down. [1yr forward P/E, by contrast, has much less correlation with long-run returns]

1) Yes but the Shiller PE will be higher, thereby (incorrectly) reducing its estimate of forward returns.

2) No, I agree the market is at above average valuation, just less extremely so than shiller PE would suggest. Though it looks cheap on Equity Risk Premium measures.

3) Yeah my objection is to the methodology not the conclusion. However I think many of those other methodologies are silly as well; for example, P/R does not make sense from an accounting standpoint (it should be EV/R). Changes in the structure of the economy have made book value metrics less relevant than historically, but I agree they are somewhat concerning.

4) Looking at historical correlations with returns introduces lookahead bias. If the market valuation doubled from here, and then remained flat for 100 years while earnings grew at their historic rate, schiller PE would remain correlated with returns, except it would retrospectively advise us to buy here.

Also, I'm having trouble replicating your numbers. Using the schiller data, I get correlations of -0.54 for CAPE vs 10yr return (real or nominal), and -0.49, -0.47 for PE vs 10yr return (real and nominal respectively). This is a small enough difference that we should prefer to use the more theoretically justified measure.

Also forward earnings estimates are not available that far back so I am sceptical of any research into their ability to forecast long-run returns! For 1-year holding periods they do about as well as trailing earnings though.

However, if we use a lookahead bias free measure, and instead of using the absolute level of PE / CAPE, we instead use the percentile of that metric, relative to its own history, the results basically reverse. Using this better measure I get -0.54 and -0.51 for PE vs -0.48 and -0.43 for CAPE. (in both cases I started the correlation in 1900 so we had a few decades of data for the percentiles to stabilize in.)

Interesting. My worry with credit-spread metrics is no-one cared about them pre-2008, so their performance is all in-sample basically. People always add new explanatory variables that explain the last crisis. However I am not an expert on this.

Philosophical economics has a some critical discussion of this and similar graphs, e.g. here and more directly here. There is also a lot of discussion of current elevation of profit margins and CAPE, which I found useful.